IJPAM: Volume 104, No. 3 (2015)


Nandita Rath
School of Mathematics and Statistics
University of Western Australia
Crawley, W.A. 6009, AUSTRALIA

Abstract. The category $FIL$ of filter spaces being isomorphic to the category of grill-determined nearness spaces has become significant in the later part of the twentieth century. During that period, a substantial completion theory has been developed using the equivalence classes of filters in a filter space. However, that completion was quite general in nature, and did not allow the finest such completion. As a result, a completion functor could not be defined on $FIL$. In this paper, this issue is partially addressed by constructing a completion that is finer than the existing completions. Also, a completion functor is defined on a subcategory of $FIL$ comprising all filter spaces as objects.

Received: August 16, 2015

AMS Subject Classification: 54D35, 54A20, 54C20

Key Words and Phrases: filter space, Cauchy map, convergence structure, $s$-map, stable completion, completion in standard form

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DOI: 10.12732/ijpam.v104i3.13 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 104
Issue: 3
Pages: 461 - 470

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